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Please check that your device is correctly connected to the wifi/internet (settings > wifi) and is plugged into a power source, also check that you have enough space in iCloud for your back up.
You can check the space available at settings > iCloud > Storage and the space needed for the next back up at Settings > iCloud > Storage > Manage Storage > BackUps > This Device > Back Up Options > Next back up Size (wait for the spinning gear icon to finish).
Assuming you meet the requirements for iCloud back up, you should try a forced shutdown to begin with, hold down the side/top and home buttons together until the device shuts down, then restart it by pressing the side/top button.
Next, try connecting the device in a new location (different WiFi network)
If your back up continues to fail, you might try turning off BackUp on your mobile device (Settings > iCloud > BackUp), restarting the device and then turning BackUp back on again.
If this doesn’t help turn BackUp off again, delete your existing back up from Settings > iCloud > Storage > Manage Storage > BackUps > This Device (scroll down to the bottom) > Delete BackUp, restart the device and then turn BackUp back on again.
If you are still unable to complete a back up, try signing out of iCloud (Settings > iCloud (scroll down to the bottom) > Sign Out (you will need to enter your password at this stage), restart the device and sign back into iCloud at Settings > iCloud.
The next thing to try would be to reset your network settings. (Settings > General > Reset > Reset Network Settings)
Resetting your network settings will clear your current cellular and wifi network settings, including saved networks, wifi passwords and any VPN settings you might use. It will affect internet connectivity but won’t impact on telephone services since these settings are auto configured by your carrier. It may take a few moments to re-enter all your network settings but it shouldn’t cause you any major problems. If you are comfortable re-entering your network settings, you may wish to try this step a little earlier in the troubleshooting procedure, say after the forced shutdown suggested above.
If this doesn't help, try turning off some items for back up in a pattern to try to establish if your problem is being caused by specific data on your device. You can do this at Settings > iCloud > Storage > Manage Storage > BackUps > This Device > Back Up Options.
If you still aren’t able to complete a back up to iCloud, you may wish to try restoring your phone which you should do by making a back up to iTunes via your computer and restoring from that.
Being able to back up to the cloud can be very useful, especially if you don't have access to a computer or have infrequent access to one, however unless you specifically need to use iCloud for back up, you will find backing up to iTunes significantly more convenient and possibly more reliable. However if you back up to iTunes be sure to encrypt the back up if you want to keep your health data and passwords etc.
More about iCloud v iTunes Back Up
